STAT 345 Midterm

Graphic

Report

• The above graphic shows shot charts for the Minnesota Timberwolves every three years from 1999 to 2024.
• The points on the graphs represent made/missed shots.
• The points on the graphs are also perfectly proportioned with the functionalized background line of the NBA court.
• Some key trends we can see as the years get more recent are:
  • Increased amount of 3 point attempts
  • Increased amount of shot attempts by or directly under the basket
  • Decreased amount of 2 point shot attempts outside of the free throw rectangle

More Details

• The shot charts are shown from 1999 to 2024, chosen specifically for 9 seasons first because of visual purposes to make a perfect square for the charts, but also because I wanted to showcase a wide range of years to show an overall trend in how shots have changed over time.
• The green points represent made shots, while the red represent missed shots. I also made them pretty opaque, in order to better see where the most overlap occurs in different regions of the court.
• In order to get the points to be graphed proportionally with the NBA court, I divided each original x and y location value by ten, as well as multiplying the x values by a negative since the original values are flipped in the nbastatR package. I also added the hoop center dimension to the y values in order to translate them to all be in bounds of the court background. One key note is that we are only looking at a little less than half of a court, since we are only interested in one team’s shots, but this may have left out a few outlying shot points that were past half court. Overall, this doesn’t affect the overall trends seen in the shot data, so the extra space showing more of a court would add did not seem necessary in this case.
• The key trends we can see all relate to the opacity of the points, meaning that where the graph is darker is where more shots were taken, making it easy to see trends especially when looking at a span of 25 years of shot data.

This section calculates an expected value for a 4 point arc in the NBA.

To calculate where a 4 point line should be on an NBA court, I needed to find the expected value for a 4 point shot. To do this, I decided to use data from the past 10 years for the Minnesota Timberwolves, because gathering shot data from every single team over many years would likely be too much to handle, especially since taking it over many years would likely result with similar findings regardless of what team is being looked at. I also decided to look at more recent years, because that makes our findings more relevant to today.

To start, I calculated the expected value for 2 and 3 point shots, which looks like this: Expected shot value (n) = (total n pointers made * n) / total n pointer attempts. From this, I got ~1.02 for 2 pointers and ~1.06 for 3 pointers. Because these values are 0.04 apart, I decided that the optimal place for a 4 point line would be where the corresponding shots line up with an expected value around 1.10, which would be an additional 0.04 above the 3 point expected value. I then calculated the expected values for 4 point shots at various distances, finding that the expected value at 27 or more feet from the hoop is ~1.16 and at 28 or more feet it is ~0.95. From this, I can conclude that the ideal distance for a 4 point arc, given that it is just a simply-shaped arc, would be at about 27.7 feet away from the hoop (which gets the expected value to be ~1.10).

One consequence of adding a 4 point line to the NBA could be that the entire nature of the game could be changed. If players now have more incentive for taking longer shots, there would most likely be less shots taken at the 3 point and especially the 2 point range. In my eyes, this would make basketball a much more offense-dominated sport, because it would make the court more spread out. Players would not go for 2 point shots as often, and the potential for rebounds and defense in that area would lessen.